MILAN, Oct 10 (Reuters) - Britain’s top share index ended at a two-month high on Tuesday after domestic banks Royal Bank of Scotland and Lloyds rose following a broker upgrade on hopes of a softer exit from the European Union.

Britain’s blue-chip FTSE 100 index was up 0.4 percent at 7,538.27 points at its close, while the more domestically-focused mid-cap index added 0.2 percent, boosted by some well-received earnings updates.

After hitting record highs in May thanks to the weakness in the pound that followed Britain’s decision to leave the EU, the rally in the FTSE has lost steam as sterling strengthened and the Bank of England turned more hawkish.

Uncertainty over Prime Minister Theresa May’s grip on leadership has fuelled worries over a hard Brexit, prompting a fresh sell-off in the pound last week and supporting internationally-exposed UK blue chips.

But the pound bounced back as May vowed to ward off challenges and was up on Tuesday after strong monthly manufacturing data reinforced expectations of a rate hike in November.

RBS was among the biggest gainers, up 1.9 percent, and Lloyds rose 0.8 percent after Credit Suisse upgraded the two stocks to “outperform” and “neutral” respectively.

“We think investor sentiment towards UK domestic bank stocks should improve over the next 12 months as a soft Brexit becomes more likely,” analysts at the Swiss bank wrote in a note.

“Our central scenario of low growth, low unemployment and moderate rate rises is supportive for domestic banks’ capital generation and we believe earnings risk is to the upside,” they added.

RBS was also supported by an upgrade from Citi which said the bank is the most geared to rising rates and has the most defensive asset mix.

Britain and its EU partners clashed on Monday over who should make the next move to unblock Brexit talks. However, May told business leaders on Monday that they could be certain there would be a two-year Brexit transition period, a source told Reuters.

Credit Suisse also downgraded internationally exposed HSBC to underperform but lifted their price target. The stock was up 1 percent.

BAE Systems, however, retreated 0.3 percent. The British defence company was set to announce up to 2,000 job cuts at plants involved in making the Eurofighter Typhoon fighter jet, whose orders have dried up.

Among mid-caps, Domino’s Pizzas rose around 9 percent, its biggest one-day gain in two years after Britain’s biggest pizza delivery firm said trading in the third quarter improved in the UK.

Pub operator Marston’s also rose, up 3.8 percent, after a well-received trading update that prompted Liberum to affirm its buy rating on the stock.

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